# Linear combination of vectors and RGB colours

- Author:
- Simona Riva

Given three vectors

*u*,*v*and*w*and three scalars*a*,*b*and*c*, the*linear combination*of those vectors is vector*d*=*au*+*bv*+*cw*In this applet*u*=(255,0,0),*v*=(0,255,0) and*w*= (0,0,255), and the scalars*a*,*b*and*c*range in [0,1]. Move the sliders and watch the resulting position of the linear combination vector. Now let's consider this vectorial problem from a different point of view.*RGB*is an*additive colour model*used to represent the colours of objects in many environments. In computers, a*RGB*colour is usually stored as a*triplet of integer numbers*in the range 0 to 255. (255,0,0) is*red*- (0,255,0) is*green*- (0,0,255) is*blue*. We can view those colours as the*vectors*in 3D space, having those components. Any other colour is obtained as a*linear combination*of these basic colours. If you*multiply*a*vector*by a*scalar*, you obtain the*same colour*, but a*different shade*of it. Move the sliders and find out where the*yellows*, or the*grey*shades are, and examine the position of the corresponding vector in the visual representation. Please note that the components of the resulting vector have been*rounded*, to match the computer requirements whenever you need to enter*RGB*triplets to define a colour. You can also use this applet as a reference to*define dynamic colours*of objects in GeoGebra.